Optimality conditions for state-constrained PDE control problems with time-dependent controls

被引:0
作者
de Los Reyes, J. C. [1 ]
Merino, P. [1 ]
Rehberg, J. [2 ]
Troeltzsch, F. [3 ]
机构
[1] EPN Quito, Dept Math, Quito, Ecuador
[2] Weierstrass Inst Angew Anal & Stochast WIAS, Berlin, Germany
[3] TU Berlin, Inst Math, Berlin, Germany
来源
CONTROL AND CYBERNETICS | 2008年 / 37卷 / 01期
关键词
parabolic equation; elliptic equation; optimal control; pointwise state constraints; sufficient optimality conditions; restricted control class;
D O I
暂无
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
The paper deals with optimal control problems for semilinear elliptic and parabolic PDEs subject to pointwise state constraints. The main issue is that the controls are taken from a restricted control space. In the parabolic case, they are R-m -vectorvalued functions of time, while they are vectors of R-m in elliptic problems. Under natural assumptions, first- and second-order sufficient optimality conditions are derived. The main result is the extension of second-order sufficient conditions to semilinear parabolic equations in domains of arbitrary dimension. In the elliptic case, the problems can be handled by known results of semi-infinite optimization. Here, different examples are discussed that exhibit different forms of active sets and where second-order sufficient conditions are satisfied at the optimal solution.
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页码:5 / 38
页数:34
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